oj.uz

Submission #227035

# Submission time Handle Problem Language Result Execution time Memory
227035 2020-04-25T22:25:51 Z abeker Matching (COCI20_matching) C++17
58 / 110
 341 ms 524292 KB 
#include <bits/stdc++.h>
using namespace std;
 
typedef pair <int, int> pii;
 
const int MAXN = 1e5 + 5;
const int offset = 1 << 17;
const int MAXV = 1.05e7 + 5;

int n;
bool sol[MAXV];
bool bio[MAXV];
int comp[MAXV];
vector <int> adj[MAXV], rev[MAXV];
stack <int> order;

inline int add_variables(int vars) {
	n += vars;
	return n - vars;
}

void add_edge(int u, int v) {
	adj[u].push_back(v);
	rev[v].push_back(u);
}

void add_implication(int u1, int neg1, int u2, int neg2) {
	add_edge(2 * u1 + neg1, 2 * u2 + neg2);
	add_edge(2 * u2 + !neg2, 2 * u1 + !neg1);
}

void dfs_forward(int x) {
	bio[x] = true;
	for (auto it : adj[x])
		if (!bio[it])
			dfs_forward(it);
	order.push(x);
}

void dfs_backward(int x, int c) {
	comp[x] = c;
	for (auto it : rev[x])
		if (!comp[it])
			dfs_backward(it, c);
}

bool two_sat() {
	for (int i = 0; i < 2 * n; i++)
		if (!bio[i])
			dfs_forward(i);
	int ptr = 0;
	for (; !order.empty(); order.pop())
		if (!comp[order.top()])
			dfs_backward(order.top(), ++ptr);
	for (int i = 0; i < 2 * n; i++) {
		if (comp[i] == comp[i ^ 1])
			return false;
		sol[i] = comp[i] > comp[i ^ 1];
	}
	return true;
}

int N;
int x[MAXN], y[MAXN];
vector <pii> tour[2 * offset];
int st[2 * offset], off[2 * offset];
vector <int> hor[MAXN], ver[MAXN];
unordered_map <int, pii> segs;
vector <int> graph[MAXN];
 
void load() {
	scanf("%d", &N);
	for (int i = 0; i < N; i++) {
		scanf("%d%d", x + i, y + i);
		hor[y[i]].push_back(i);
		ver[x[i]].push_back(i);
	}
}
 
void insert(int x, int lo, int hi, int from, int to, int var, int height) {
	if (lo >= to || hi <= from)	
		return;
	if (lo >= from && hi <= to) {
		tour[x].push_back({height, var});
		return;
	}
	int mid = (lo + hi) / 2;
	insert(2 * x, lo, mid, from, to, var, height);
	insert(2 * x + 1, mid, hi, from, to, var, height);
}
 
inline int get_id(int node, int x) {
	return x < off[node] ? st[node] + x : tour[node][x - off[node]].second;
}
 
void add_clause(int x, int u, int v) {
	if (u < off[x] + tour[x].size())
		add_implication(get_id(x, u), 0, get_id(x, v), 0);
}
	
void init(int x) {
	if (tour[x].empty())
		return;
	off[x] = 1;
	sort(tour[x].begin(), tour[x].end());
	while (off[x] < tour[x].size())
		off[x] *= 2;
	st[x] = add_variables(2 * off[x]);
	for (int i = 0; i < off[x]; i++) {
		add_clause(x, 2 * i, i);
		add_clause(x, 2 * i + 1, i);
	}
}
 
int get_bounds(int x, int val) {
	int lo = 0, hi = tour[x].size();
	while (lo < hi) {
		int mid = (lo + hi) / 2;
		if (tour[x][mid].first >= val)
			hi = mid;
		else
			lo = mid + 1;
	}
	return lo;
}
 
void update(int node, int from, int to, int var) {
	from += off[node];
	to += off[node];
	while (from < to) {
		if (from % 2) 
			add_implication(get_id(node, from++), 0, var, 1);
		if (to % 2) 
			add_implication(get_id(node, --to), 0, var, 1);
		from /= 2;
		to /= 2;
	}
}
 
void add_intersections(int x, int down, int up, int var) {
	for (x += offset; x; x /= 2) 
		if (off[x])
			update(x, get_bounds(x, down), get_bounds(x, up + 1), var);
}
 
void bye() {
	puts("NE");
	exit(0);
}
 
void solve() {
	for (int i = 1; i < MAXN; i++) 
		if (hor[i].size() == 2) {
			int tmp = add_variables(1);
			segs[tmp] = {hor[i][0], hor[i][1]};
			int l = MAXN, r = 0;
			for (auto it : hor[i]) {
				graph[it].push_back(tmp);
				l = min(l, x[it]);
				r = max(r, x[it]);
			}
			insert(1, 0, offset, l, r + 1, tmp, i);
		}
	
	for (int i = 0; i < 2 * offset; i++)
		init(i);
	
	for (int i = 1; i < MAXN; i++) 
		if (ver[i].size() == 2) {
			int tmp = add_variables(1);
			segs[tmp] = {ver[i][0], ver[i][1]};
			int l = MAXN, r = 0;
			for (auto it : ver[i]) {
				graph[it].push_back(tmp);
				l = min(l, y[it]);
				r = max(r, y[it]);
			}
			add_intersections(i, l, r, tmp);
		}
	
	for (int i = 0; i < N; i++) 
		if (!graph[i].empty())
			add_implication(graph[i][0], 1, graph[i][1 % graph[i].size()], 0);
		else
			bye();
	
	if (!two_sat())
		bye();
	
	puts("DA");
	for (auto it : segs)
		if (sol[2 * it.first])
			printf("%d %d\n", it.second.first + 1, it.second.second + 1);
}
 
int main() {
	double timer = clock();
	load();
	solve();
	fprintf(stderr, "%lf\n", (clock() - timer) / CLOCKS_PER_SEC);
	return 0;
}

Compilation message

matching.cpp: In function 'void add_clause(int, int, int)':
matching.cpp:97:8: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  if (u < off[x] + tour[x].size())
      ~~^~~~~~~~~~~~~~~~~~~~~~~~~
matching.cpp: In function 'void init(int)':
matching.cpp:106:16: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
  while (off[x] < tour[x].size())
         ~~~~~~~^~~~~~~~~~~~~~~~
matching.cpp: In function 'void load()':
matching.cpp:72:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
  scanf("%d", &N);
  ~~~~~^~~~~~~~~~
matching.cpp:74:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
   scanf("%d%d", x + i, y + i);
   ~~~~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 316 ms 507000 KB Output is correct
2 Correct 265 ms 507120 KB Output is correct

Subtask #2
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 316 ms 507000 KB Output is correct
2 Correct 265 ms 507120 KB Output is correct
3 Correct 260 ms 506976 KB Output is correct
4 Correct 260 ms 507000 KB Output is correct
5 Correct 299 ms 507000 KB Output is correct
6 Correct 298 ms 507268 KB Output is correct
7 Correct 341 ms 507000 KB Output is correct

Subtask #3
7.0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 316 ms 507000 KB Output is correct
2 Correct 265 ms 507120 KB Output is correct
3 Correct 260 ms 506976 KB Output is correct
4 Correct 260 ms 507000 KB Output is correct
5 Correct 299 ms 507000 KB Output is correct
6 Correct 298 ms 507268 KB Output is correct
7 Correct 341 ms 507000 KB Output is correct
8 Correct 275 ms 507256 KB Output is correct
9 Correct 301 ms 507128 KB Output is correct
10 Correct 264 ms 507256 KB Output is correct
11 Correct 283 ms 507256 KB Output is correct
12 Correct 289 ms 507128 KB Output is correct

Subtask #4
40.0 / 40.0

# Verdict Execution time Memory Grader output
1 Correct 316 ms 507000 KB Output is correct
2 Correct 265 ms 507120 KB Output is correct
3 Correct 260 ms 506976 KB Output is correct
4 Correct 260 ms 507000 KB Output is correct
5 Correct 299 ms 507000 KB Output is correct
6 Correct 298 ms 507268 KB Output is correct
7 Correct 341 ms 507000 KB Output is correct
8 Correct 275 ms 507256 KB Output is correct
9 Correct 301 ms 507128 KB Output is correct
10 Correct 264 ms 507256 KB Output is correct
11 Correct 283 ms 507256 KB Output is correct
12 Correct 289 ms 507128 KB Output is correct
13 Correct 279 ms 510328 KB Output is correct
14 Correct 276 ms 510328 KB Output is correct
15 Correct 272 ms 510328 KB Output is correct
16 Correct 293 ms 510324 KB Output is correct
17 Correct 318 ms 510328 KB Output is correct
18 Correct 281 ms 510488 KB Output is correct
19 Correct 275 ms 510328 KB Output is correct
20 Correct 278 ms 510328 KB Output is correct
21 Correct 275 ms 510328 KB Output is correct
22 Correct 270 ms 510200 KB Output is correct
23 Correct 294 ms 510184 KB Output is correct
24 Correct 322 ms 509948 KB Output is correct

Subtask #5
0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 316 ms 507000 KB Output is correct
2 Correct 265 ms 507120 KB Output is correct
3 Correct 260 ms 506976 KB Output is correct
4 Correct 260 ms 507000 KB Output is correct
5 Correct 299 ms 507000 KB Output is correct
6 Correct 298 ms 507268 KB Output is correct
7 Correct 341 ms 507000 KB Output is correct
8 Correct 275 ms 507256 KB Output is correct
9 Correct 301 ms 507128 KB Output is correct
10 Correct 264 ms 507256 KB Output is correct
11 Correct 283 ms 507256 KB Output is correct
12 Correct 289 ms 507128 KB Output is correct
13 Correct 279 ms 510328 KB Output is correct
14 Correct 276 ms 510328 KB Output is correct
15 Correct 272 ms 510328 KB Output is correct
16 Correct 293 ms 510324 KB Output is correct
17 Correct 318 ms 510328 KB Output is correct
18 Correct 281 ms 510488 KB Output is correct
19 Correct 275 ms 510328 KB Output is correct
20 Correct 278 ms 510328 KB Output is correct
21 Correct 275 ms 510328 KB Output is correct
22 Correct 270 ms 510200 KB Output is correct
23 Correct 294 ms 510184 KB Output is correct
24 Correct 322 ms 509948 KB Output is correct
25 Runtime error 338 ms 524292 KB Execution killed with signal 9 (could be triggered by violating memory limits)
26 Halted 0 ms 0 KB -